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COMMENTS ON THE SURVEY BY BALAKRISHNAN AND ZHAO

Published online by Cambridge University Press:  13 August 2013

Moshe Shaked
Moshe Shaked*
Affiliation:
Department of Mathematics, University of AZ, Tucson, Arizona 85721, USA E-mail: shaked@math.arizona.edu
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Extract

N. Balakrishnan and Peng Zhao have prepared an outstanding survey of recent results that stochastically compare various order statistics and some ranges based on two collections of independent heterogeneous random variables. Their survey focuses on results for heterogeneous exponential random variables and their extensions to random variables with proportional hazard rates. In addition, some results that stochastically compare order statistics based on heterogeneous gamma, Weibull, geometric, and negative binomial random variables are also given. In particular, the authors of have listed some stochastic comparisons that are based on one heterogeneous collection of random variables, and one homogeneous collection of random variables. Personally, I find these types of comparisons to be quite fascinating. Balakrishnan and Zhao have done a thorough job of listing all the known results of this kind.

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Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 4 , October 2013 , pp. 445 - 449
Copyright
Copyright © Cambridge University Press 2013 

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